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Answer: 7

Step-by-step explanation:

For c, we are given this sum from 1 to 3 of . 1/2 is a constant , therefore, we can move it outside of the summation.

*I hope you can understand what I'm saying. I can't figure out how to type in summations into the equations section.

1/2∑₁³n²

This means you would multiply the sum of n² from 1 to 3 by 1/2.

We are told n=1 to n=3 so we would plug 1, 2, 3 into n.

1²=1

2²=4

3²=9

We would add them together since that is what the sum sign tells us to do.

1+4+9=14

Now that we know the sum, we multiply it with 1/2

14/2=7

Answer:

a) The requirements is that each trial can only have two outcomes(success/failure), and each trial has the same probability of a success, that is, they are independent of each other.

In this problem, for each person, either they are allergic to some kind of food, or they are not. The probability of a person being allergic is independent of any other people. So this situations meets all these requirements.

b) The expected value is 30 and the standard deviation is 5.31.

c) Close to 0% probability that none of the 500 employees has a food allergy

Step-by-step explanation:

For each adult, there are only two possible outcomes. Either they have food allergy, or they do not. The probability of an adult having allergy is independent of other adults. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which is the number of different combinations of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.

The expected value of the binomial distribution is:

The standard deviation of the binomial distribution is:

6% of American adults have a food allergy

This means that

500 employees.

This means that

(a) What are the assumptions/requirements of a Binomial distribution? Does this situation meet all these requirements?

The requirements is that each trial can only have two outcomes(success/failure), and each trial has the same probability of a success, that is, they are independent of each other.

In this problem, for each person, either they are allergic to some kind of food, or they are not. The probability of a person being allergic is independent of any other people. So this situations meets all these requirements.

(b) What are the expected value and standard deviation of X (i.e., of the population)?

The expected value is 30 and the standard deviation is 5.31.

(c) What is the probability that none of the 500 employees has a food allergy?

This is P(X = 0).

Close to 0% probability that none of the 500 employees has a food allergy

Answer:

G

Step-by-step explanation:

Try to understand what this equation is saying and what plugging in different values would represent.

At x=0, b(0)=850; which means the initial balance is $850. So H is incorrect.

At x=1, b(1)=871.25; which means that after 1 year, the initial balance will have increase to $871.25. So J is incorrect.

Since the initial vacation of 850 is being multiplied by a factor which is greater than one, the balance will be increased each year. So F is incorrect.

Finally, if we look at the factor by which we are multiplying, do a simple Algebraic step, and convert it into percentages we get:

1.025 = (1 + 0.025) = 100% + 2.5%

Essentially this is showing us that the balance will increase by 2.5% on however much is in the account each year.

So G is your answer.

Answer:  B) -1/2

Explanation: Parallel lines have the same slopes, but different y intercepts.

Answer:

the slope of the red line is also -1/2

Step-by-step explanation:

Answer:

Commutative property of multiplication is shown above. This is because no matter how you put them, the answer will still be 140  

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